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# The equation of the line that goes through the point (2,3) and is parallel to the 4x+3y=3 can be written in the form y=mx+b where m&nbs

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The equation of the line that goes through the point (2,3) and is parallel to the 4x+3y=3 can be written in the form y=mx+b where m is: and b is:

Dec 12, 2018

#1
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Rewrite   4x+3y=3

3y=-4x+3

y = -4/3x +1      where =-4/3 is the slope....parallel line will have same slope

y = -4/3 x + b    includes 2,3

3 = -4/3 (2) + b

3+8/3 = b

b = 5 2/3

so NEW line is    y = -4/3x + 5 2/3      m = -4/3   b = 5  2/3

Dec 12, 2018
#2
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We can make $$4x+3y=3$$ into $$y=mx+b$$ form! We need to isolate $$y$$ .

$$3y=-4x+3, y=-\frac{4}{3}x+1$$

However, the line goes through (2, 3) so the y-intercept may not be 1! Let's substitute.

$$3=-\frac{4}{3}\times 2+b, 3=-\frac{8}{3}+b, b=17/3$$ and m=-4/3.

You are very welcome!

:P

Dec 12, 2018